{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Backpropagation\n",
    "\n",
    "The most popular way to train neural networks is with what is called the method of _backpropagation_. In it, we look to compute $\\forall l\\in\\{1,\\ldots,L\\}, i,j. \\frac{\\partial E_n}{\\partial w_{ji}^{(l)}}$\n",
    "\n",
    "The required steps for backpropgation algorithm are:\n",
    "1. Forward propagate an input $x_n$\n",
    "2. Evaluate $\\forall k. \\delta_k^{L}$ at the output layer $L$\n",
    "3. Backpropagate $\\forall l\\neq L, k. \\delta_k^{l}$\n",
    "4. Evaluate $\\forall i,j. \\frac{\\partial E_n}{w_{i,j}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import requests\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import randn, seed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "np.set_printoptions(linewidth=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will consider the example in section 5.3.2 of prml:\n",
    "![Figure 5.1](./imgs/f51.png)\n",
    "\n",
    "A two-layered neural network with sum of squares error as the error function; with linear output activation units, i.e., $y_k = a_k$ and; tanh (hyperbolic tangent) activation functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "url = \"https://www.itl.nist.gov/div898/strd/nls/data/LINKS/DATA/Gauss2.dat\"\n",
    "beacon = \"Data:\"\n",
    "r = requests.get(url)\n",
    "data = r.text\n",
    "data = data[data.rfind(beacon) + len(beacon):]\n",
    "data = np.array([v.split() for v in data.split(\"\\n\")][1:-1]).astype(\"float\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11f513a90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 375
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data[:, 1], data[:,0], s=0.4, c=\"tab:red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have a two-layered neural network with $H$ hidden units; an input unit and a single output unit. The explicit form for this neural network is of the form:\n",
    "\n",
    "$$\n",
    "    f(x_n, {\\bf w}^{1}, {\\bf w}^{2}) = \\sum_{k=1}^H w_{1k}^{(2)} h\\left(w_{k1}^{(1}x_n + w_{k0}^{(1)}\\right) + w_{10}^{(2)}\n",
    "$$\n",
    "\n",
    "Suppose further that this neural network has a tanh activation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(314)\n",
    "w0 = randn(4, 2) / 10\n",
    "w1 = randn(1, 5) / 10\n",
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "xn = np.array([[.5, 1]]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ],\n",
       "       [ 0.08628562],\n",
       "       [-0.02808545],\n",
       "       [ 0.0420584 ],\n",
       "       [ 0.02707626]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z1 = np.r_[[[1]], np.tanh(w0 @ xn)]\n",
    "z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = w1 @ z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_prop(x, w1, w2):\n",
    "    a1 = w1 @ x\n",
    "    z1 = np.r_[[[1]], np.tanh(a1)]\n",
    "    a2 = w2 @ z1\n",
    "    return a1, a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 0.08650072],\n",
       "        [-0.02809284],\n",
       "        [ 0.04208323],\n",
       "        [ 0.02708287]]), array([[-0.07429066]]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forward_prop(xn, w0, w1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, t  = data[0]\n",
    "x = np.array([[x, 1]]).T\n",
    "a1, a2 = forward_prop(x, w0, w1)\n",
    "# changes in weight at the second layer \n",
    "z1 = np.r_[[[1]], np.tanh(a1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = a2.ravel()[0] - t\n",
    "d0 = (1 - z1.T ** 2) * w1 * d1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.88302248],\n",
       "       [-0.82587532],\n",
       "       [-0.88302236],\n",
       "       [ 0.88302246],\n",
       "       [ 0.85824532]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Derivative at the second layer\n",
    "d1 * z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-9.31405337e-01,  6.66301529e-07,  4.86134130e-07,  2.37704994e-01],\n",
       "       [-9.54428442e-03,  6.82771619e-09,  4.98150721e-09,  2.43580746e-03]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Derivative at the first layer\n",
    "x @ d0[:, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.06842732,  0.09455747, -0.01929578, -0.10202277, -0.05843618]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Value updates at the second layer\n",
    "w1 - alpha * (d1 * z1).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.0259226 ,  0.07829189],\n",
       "       [ 0.0852285 , -0.0707071 ],\n",
       "       [-0.09316572,  0.08866609],\n",
       "       [-0.02455602,  0.038148  ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Value update at the first layer\n",
    "w0 - alpha * (x @ d0[:, 1:]).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(314)\n",
    "nhidden = 50\n",
    "w0 = randn(nhidden, 2)\n",
    "w1 = randn(1, nhidden + 1)\n",
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "that = []\n",
    "epochs = 4\n",
    "for e in range(epochs):\n",
    "    for t, x in data:\n",
    "        x = np.array([[1, x]]).T\n",
    "        a1, a2 = forward_prop(x, w0, w1)\n",
    "        # changes in weight at the second layer \n",
    "        z1 = np.r_[[[1]], np.tanh(a1)]\n",
    "\n",
    "        d1 = a2.ravel()[0] - t\n",
    "        d0 = (1 - z1.T ** 2) * w1 * d1\n",
    "\n",
    "        w1 = w1 - alpha * (d1 * z1).T\n",
    "        w0 = w0 - alpha * (x @ d0[:, 1:]).T \n",
    "for t, x in data:\n",
    "    x = np.array([[1, x]]).T\n",
    "    a1, a2 = forward_prop(x, w0, w1)\n",
    "    that.append(a2.ravel()[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12790b3c8>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 377
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(that)\n",
    "plt.plot(data[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 379
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(that - data[:,0])\n",
    "plt.axhline(y=0, c=\"black\")\n",
    "plt.grid(alpha=0.3, linestyle=\"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "that = []\n",
    "for e in range(1):\n",
    "    for t, x in data:\n",
    "        x = np.array([[1, x]]).T\n",
    "        a1, a2 = forward_prop(x, w0, w1)\n",
    "        # changes in weight at the second layer \n",
    "        z1 = np.r_[[[1]], np.tanh(a1)]\n",
    "\n",
    "        d1 = a2.ravel()[0] - t\n",
    "        d0 = (1 - z1.T ** 2) * w1 * d1\n",
    "        if e == 0:\n",
    "            that.append(a2.ravel()[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x127af5780>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 377
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(that)\n",
    "plt.plot(data[:,0])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
